At the 1988 Summer Olympics in Busan, South of Korea, he finished in 2nd place in the Soling class along with his partners William Baylis and Robert Billingham.
Kostecki started his sailing career in the windy and tide-swept waters of San Francisco Bay, California. That year, he was then named United States Rolex Yachtsman of the Year. He also sailed the Whitbread Round the World Race in 1997/1998.
Kostecki became very popular in Europe as skipper and helmsman of the German yacht Illbruck in the Volvo Ocean Race 2001/2002.
He led the team that was based in Leverkusen to an overwhelming victory in the arguably toughest sailing race around the world. Of notable interest was the fact that Illbruck set the world 24 hours speed record for monohulls.
The record of 484 nautical miles was completed at 20:02 on April 30 during Legal 7 of the Volvo Ocean Race and was confirmed by the World Sailing Speed Record Council. This sparked an unprecedented sailing boom in Germany that led to thousands of sailing fans and Illbruck supporters awaiting Kostecki and his crew finishing their last leg from Gothenburg to Kiel.
In 2002, Kostecki was named United States Rolex Yachtsman of the Year for the second time.
After a short employment with the Bayerische Motoren Werke Oracle America’s Cup Team he joined team Ericsson for the next Volvo Ocean Race (2005/2006). He was also Ericsson’s designated skipper for the next Race (2008/2009) but resigned from his position in August 2007 for family reasons. The next America’s cup match took place between the defender, the Swiss team Alinghi, and Bayerische Motoren Werke Oracle, in Valencia (Spain) in February 2010.